The lapping and polishing of large aspheric astro-mirrors is a very time consuming task since it is most difficult to obtain the exact form of the mirror with the accuracy over the entire mirror surface of fractions of the wavelength required for observing in the optical spectral range. Such fractions of the wavelength can typically be 10-50 nm RMS.
One usually proceeds by first lapping and polishing a spherical surface whereby a radius of curvature is selected which comes closest to the desired aspheric surface. Thereafter, the aspheric deformation is polished into the mirror with tools that are very much smaller than the mirror surface.
This polishing work is continuously interrupted by interferometric tests in which remaining residual errors are detected. The closer one comes to the objective, the more the work shifts from the removal of rotational symmetrical errors to the removal of nonsymmetrical local residual errors.
An article entitled "Segmented Mirror Polishing Experiment" in the publication "Applied Optics", Volume 21, Number 3 (1982), pages 561-564 discloses that the described process can be partially automated in that the tool is computer-control guided over the surface to be observed such that the dwell time of the tool varies at different locations of the surface and is dependent upon the material to be removed from said locations.
However, with this method, the different subareas of the workpiece are sequentially worked by means of a relatively small tool thereby making the processing time very long.
Furthermore, it is very difficult to work the edge portions of the workpiece with this method since the working action of the tool in these regions is very irregular.